If the vectors a = i-j+2k, b = 2i+4j+k and c = ai+j+bk
If the vectors a = i - j + 2k, b = 2i + 4j + k and c = ai + j + bk are mutually orthogonal, then (a,b) =
- (-2,3)
- (3,-2)
- (-3,2)
- (2,-3)
Answer
a = i - j + 2k, b = 2i + 4j + k and c = ai + j + bk
Given, a, b and c are mutually orthogonal
a.c = 0
a - 1 + 2b = 0
a + 2b = 1
b.c = 0; 2a + 4 + b = 0
2a + b = -4
The correct option is C.